This paper considers the real-time control of a class of complex continuous nonlinear systems with an increasing requirement on control accuracy and unknown dynamics at the start time due to their complex dynamics and uncertainties. A Koopman approximate model-based adaptive MPC design using the Lyapunov technique is explored. Specifically, the nonlinear system is modeled/transformed into a linear model in a lifting space with the Koopman operator. A recursive update of the approximator is provided by which the parameters set of the approximator is in a nested form and a shrinking of the boundary of the approximator’s mismatch from the real system is obtained. Also, based on the Koopman model and its mismatch boundary, a sufficient condition that ensures the states of the nonlinear system eventually converge to a small neighborhood of the origin is deduced. An FCCU example is employed to show the effectiveness of the proposed control law.